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Solution to Exercise 3
(a) Hmm. I trim my fingernails about once a month, and they've grown out about an eighth of an inch each time, so my fingernails grow at (1/8 inch/mo) * (12 mo/yr) = 1.5 inches per year. (b) Hmm. I get my hair cut about once a month, and my hair has grown out about an inch each time, so my hair grows at about (1 inch/mo) * (12 mo/yr) = 12 inches per year. (c) Since I've estimated in all my calculations (including for Exercise 2 above) using "numerical sense," an answer that's twice as big or twice as small as another answer can be considered approximately the same. Since I calculated above that the continents are moving about 3 inches per year, I feel confident enough to assert that my fingernails grow at roughly the same speed as the continents drift! My hair apparently grows faster, though - 12 inches per year is a somewhat larger value than 3 inches per year. Again, the key words are "about," "approximately," and "roughly." If you challenged my assertion that my hair grows faster than the continents drift, I wouldn't be insulted in the least; you need only convince me that one or more of my estimates didn't make numerical sense. Perhaps you may assert that my hair grows only a quarter inch a month. Then, I might reply that if my hair grew only a quarter inch, I wouldn't bother to get it cut. So the numerical sense debates move forward - and we learn something about our universe in the meantime! |